A lane keeping assist device for a vehicle includes a steering control device, a detection device for lane of travel for assisting travel of the vehicle in a lane of travel in accordance with detection results and steering state and traveling state of the vehicle. Road curvature in a direction the vehicle traveling in is estimated on the basis of a first road curvature calculated on the basis of calculation result of a vehicle state amount calculation device and detection result of a state detection device, and a second road curvature calculated on the basis of positional coordinates by a predetermined distance in the direction the vehicle traveling in detected by a navigation system NAV. Target state amount is set on the basis of the road curvature and the steering state and traveling state of the vehicle.